1. Field of the Invention
The invention relates to a digital signal processing arrangement for generating digital output signal samples y(n) which are each formed by the sum of a given plurality of first signal samples x(n) which are each modified by one out of a plurality of second signal samples z(n), the signal processing arrangements comprising:
FIRST MEANS FOR SERIALLY SUPPLYING THE FIRST SIGNAL SAMPLES X(N);
SECOND MEANS FOR SERIALLY SUPPLYING THE SECOND SIGNAL SAMPLES Z(N);
MULTIPLYING MEANS HAVING AN INPUT CIRCUIT AND AN OUTPUT CIRCUIT;
FIRST COUPLING MEANS FOR COUPLING THE INPUT CIRCUIT OF THE MULTIPLYING MEANS TO THE FIRST AND THE SECOND MEANS;
ADDING MEANS COUPLED TO SAID MULTIPLYING MEANS.
2. Description of the Prior Art
When designing systems for digital signal processing the designer is often confronted by the task to implement an ambiguously given mathematical operation such as a digital convolution in filters or digital correlation in correlators in such a way that given requirements are satisfied which are imposed on, for example, the complexity of the equipment on the one hand and the internal processing speed on the other hand. These requirements are often imposed compulsorily by the designer to enable the realization of the system under consideration as one integrated circuit on a semiconductor body, with a given maximum complexity and processing speed or as a computing instruction (algorithm) in a micro-processor with given internal structure and given maximum processing speed.
The invention is the result of investigations in the field of modems which are used to enable the transmission of synchronous data signals over existing telephone channels and in which the data signals are subjected to several processing operations, including filtering.
A frequently used digital filter is the non-recursive digital filter with which in response to a digital input signal x(n) wherein (-.infin.&lt; n &lt; .infin. ) and in response to a plurality of mutually different coefficients z(n) wherein (0 .ltoreq. n .ltoreq. N-1) a digital output signal y(n) with (-.infin. &lt; n &lt; .infin. ) is obtained. The relation between x(n), z(n) and y(n) being given by the expression ##EQU1##
Another processing operation whose mathematical representation is greatly identical to expression (1) is encountered in the calculation of the correlation function R(m) of two digital signals u(n) and v(n). This processing operation can be represented by ##EQU2## In what follows hereinafter only the digital filter processing will be considered, however, what follows hereinafter also applies to digital correlation or other processes which consist of forming the sum of a finite plurality of products of pairs of numbers.
In prior art non-recursive digital filters N-multiplications of pairs of numbers z(i) and x(n-i) and N additions of the product thus obtained are performed for calculating one output signal sample y(n) in accordance with the expression (1). This may be accompanied by an exchange between the number of multipliers which is used and the total time T.sub.tot which is required for calculating one output signal sample. When using V multipliers (1 .ltoreq. V .ltoreq. N) which can each perform a multiplication in a time T.sub.m and an accumulator which can perform an addition in a time T.sub.a it applies that: EQU T.sub.tot = (N/V) .multidot. T.sub.m + N.T.sub.a ( 3)
wherein for simplicity it is assumed that N can be divided by V; if this is not the case then in expression (3) the factor N/V must be replaced by the smallest integer which exceeds N/V.
In, for example, data transmission systems intended for transmitting synchronous data signals filters are commonly used at the transmitter end to which an input signal is applied which can assume only a limited number of mutually different values. These values are determined by the so-called "Signal constellation" of the system (see reference 1). These values may, for example, be selected from the set (-3,-1,+1,+3) or from the set (-5,-3,-.sqroot.2, 0+ .sqroot.2,+3,+5).